伤城文章网 >  > 河南省安阳二中高二数学最新学案 第3章 第1课时 《不等关系》(学生版)(人教A版必修5)

河南省安阳二中高二数学最新学案 第3章 第1课时 《不等关系》(学生版)(人教A版必修5)


▁▂▃▄▅▆▇█▉▊▋▌精诚凝聚 =^_^= 成就梦想 ▁▂▃▄▅▆▇█▉▊▋▌
第三章 不等式

一、知识结构

一元二次不 等式

与另两个"二次"的 关系
不等式的解法
不等式的应用

学习 札记

不等关 系

不等式 (组)

二元一次不等 式(组)

表示的平面区 域
线性规划
证明不等式

基本不等 式

求函数最值 实际应用

二、重点难点 重点:一元二次不等式的解法;二元一次不等式组表示的平面区域及线性规划问题; 利用基本不等式进行不等式证明与求函数的最值. 难点:含参不等式的解法,线性规划中最优整数解的求法,不等式证明.

▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓

▁▂▃▄▅▆▇█▉▊▋▌精诚凝聚 =^_^= 成就梦想 ▁▂▃▄▅▆▇█▉▊▋▌

3.1 不等关系

【学习导航】 知识网络
实际问 题

寻找不等关 系

二次不等式

用不等式 表示

一元二次不 等式

二元一次不等

式组
学习要求

1.通过具体情境, 感受在观察现实世界时和日常生活中存在着的大量不等关系, 了

解不等式(组)的实际背景.

2.经历由实际问题建立数学模型的过程, 体会其基本方法.

3.总结建立不等式模型的基本思路.

4.提高观察、抽象的能力.

【课堂互动】

自学评价

1.不等号有哪些?

【答】

2.不等关系的含义:

【答】

【精典范例】

例 1:某博物馆的门票每位 10 元, 20 人以上(含 20 人)的团体标 8 折优惠, 那么不足 20

人时, 应该选择怎样的购票策略?

【解】

点评:列式的前提是:设自变量,找不等关系. 例 2:某杂志以每本 2 元的价格发行时, 发行量为 10 万册, 经过调查, 若价格每提高 0.2 元, 发行量就减少 5000 册, 要使杂志社的销售收入大于 22.4 万元, 每本杂志的价格应 定在怎样的范围内. 【解】
▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓

▁▂▃▄▅▆▇█▉▊▋▌精诚凝聚 =^_^= 成就梦想 ▁▂▃▄▅▆▇█▉▊▋▌

点评:若设每本杂志价格为 x 元,则有 x[10- 5 (x-2)]>22.4,化简略.
2 例3.下表给出了 X、Y、Z 三种食物的维生素的含量及成本:

维生素 A(单位 /kg)

维生素 B(单位 /kg)

成本(元/kg)

X

300

700

5

Y

500

100

4

Z

300

300

3

某人欲将这三种食物混合成 100kg 的食品, 要使混合食品中至少含 35000 单位的维生

素 A 及 40000 单位的维生素 B , 设 X , Y 这两种食物各取 x kg , ykg , 那么 x , y 应满足怎样的

关系?

点评:列出的是二元一次不等式组,事实上,这里的 x,y 与 100–x - y 还都应该大 于等于0.
思维点拔:
1. 不等式(组)是刻画不等关系的数学模型.

▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓

▁▂▃▄▅▆▇█▉▊▋▌精诚凝聚 =^_^= 成就梦想 ▁▂▃▄▅▆▇█▉▊▋▌

2. 建立不等式模型的基本思路: (1)找出不等关系 (2)语言化不等关系 (3)设变量后,数量化不等关系
追踪训练
1. b 克糖水中有 a 克糖 (b>a>0) , 若再 变甜了, 还是变淡了?

听课 随笔

(列出不等式(组)) 添上 m 克糖 (m>0), 则糖水

2. 时代超市将进货单价为 80 元的商品 个, 经过调查, 己知这种商品每个涨价 1 元, 使时代超市销售此商品的收入大于 4320 元, 围内?

按 90 元一个出售时能卖 400 其销售量就减少 20 个, 要 商品价格应定在怎样的范

▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓


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